Suppose \(a,b,c,\) and \(d\) are constants such that the following holds for all real numbers \(x\) such that all denominators are nonzero:
\[\begin{align}
& \frac{10}{x(x+10)}+\frac{10}{(x+5)(x+15)}+\frac{10}{(x+10)(x+20)} \\
&+ \frac{10}{(x+15)(x+25)}+\frac{10}{(x+20)(x+30)} \\
&= \frac{a(x^2+30x+75)}{x(x+b)(x+c)(x+d)}.
\end{align} \]
What is the value of \(a+b+c+d?\)